AP Physics C: Mechanics College Board

Gravitational Forces

Gravitational Forces

Key Terms

• Gravity: A force of attraction between all mass, particularly evident between large bodies such as the Earth and Moon.
• Mass: The amount of matter in an object. Immune to changes in volume or density.
• Weight: The force of gravity acting on a mass. Changes with the strength of the gravitational field.
• Gravitational field strength (g): The force of gravity per unit mass at a point in a gravitational field.

Newton's Law of Universal Gravitation

• Every object in the universe attracts every other object with a force directed along the line of centres for the two objects.
• This force is proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between the centres of the two objects.
• The mathematical representation is: F = G(m1 * m2) / r^2
  • F is the force of gravity (measured in newtons)
  • G is the gravitational constant
  • m1 and m2 are the masses of the objects
  • r is the distance between the centres of the two objects

Gravitation and Weight

• An object’s weight refers to the force with which it is pulled toward the centre of the Earth due to gravity.
• The weight can be calculated using W = mg, where:
  • W is weight (measured in newtons)
  • m is the mass of the object (measured in kilograms)
  • g is the gravitational field strength (measured in N/kg)
• On Earth, g is approximately 9.81 N/kg. Therefore, an object with a mass of 1 kg has a weight of 9.81 N on Earth.

Gravitational Field Strength

• Gravitational field strength is the force of gravity per unit mass.
• It varies based on location, being strongest at the surface of an object and decreasing as you move further away.
• The formula to compute gravitational field strength is: g = F/m, where:
  • g is the gravitational field strength (measured in N/kg)
  • F is the gravitational force (measured in newtons)
  • m is the mass of the object experiencing the force (measured in kilograms)

Importance of Understanding Gravitational Forces

• Gravitational forces are fundamental to many aspects of everyday life and scientific study, from how objects fall to the ground to the prediction of planetary orbits.
• Understanding gravity and its effects can help solve real-world problems, such as the construction of buildings and bridges, and it also forms the basis for exploring other areas of physics, such as relativity.